A Regularized Affine-Scaling Trust-Region Method for Parametric Imaging of Dynamic PET Data

2021 ◽  
Vol 14 (1) ◽  
pp. 418-439
Author(s):  
S. Crisci ◽  
M. Piana ◽  
V. Ruggiero ◽  
M. Scussolini
Keyword(s):  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Parametric Imaging ◽  
Dynamic Pet ◽  
Region Method

Nonmonotone conic trust region method with line search technique for bound constrained optimization

2019 ◽  
Vol 53 (3) ◽  
pp. 787-805
Author(s):  
Lijuan Zhao
Keyword(s):  
Constrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Search Technique ◽  
Region Method ◽  
Bound Constrained Optimization ◽  
Line Search Technique

In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.

scholarly journals Computational approaches for parametric imaging of dynamic PET data

2019 ◽  
Author(s):  
S Crisci ◽  
M Piana ◽  
V Ruggiero ◽  
M Scussolini
Keyword(s):  
Numerical Optimization ◽  
Trust Region Method ◽  
Trust Region ◽  
Nonlinear Least Squares ◽  
Affine Scaling ◽  
Parametric Imaging ◽  
Simulation Framework ◽  
Functional Images ◽  
Ill Posed ◽  
Newton Scheme

AbstractParametric imaging of nuclear medicine data exploits dynamic functional images in order to reconstruct maps of kinetic parameters related to the metabolism of a specific tracer injected in the biological tissue. From a computational viewpoint, the realization of parametric images requires the pixel-wise numerical solution of compartmental inverse problems that are typically ill-posed and nonlinear. In the present paper we introduce a fast numerical optimization scheme for parametric imaging relying on a regularized version of the standard affine-scaling Trust Region method. The validation of this approach is realized in a simulation framework for brain imaging and comparison of performances is made with respect to a regularized Gauss-Newton scheme and a standard nonlinear least-squares algorithm.

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